X-ray ct apparatus, x-ray ct apparatus afterglow correction method, and afterglow correction program

ABSTRACT

An X-ray CT apparatus including an X-ray source for applying X-rays to an object, an X-ray detector arranged to face the X-ray source for determining the amount of transmitted X-rays of the object as projection data, basic-data acquisition means for acquiring response data of the projection data as basic data with no object present in advance every time the image of the object is acquired, analyzing means for analyzing an afterglow component of the acquired basic data into a plurality of time constants and their component ratios, storage means for storing the analyzed time constants and component ratios, correcting means for extracting an afterglow component of the projection data on the basis of the stored time constants and component ratios during radiography of the object and removing the extracted afterglow component of the projection data from the projection data to produce corrected projection data, reconstructing means for reconstructing an image using the produced corrected projection data, and display means for displaying the reconstructed image.

TECHNICAL FIELD

The present invention relates to an X-ray CT apparatus and a method anda program for correcting the afterglow of the same.

BACKGROUND ART

A solid-state type X-ray detector of X-ray CT apparatus is becomingdominant. Since the sensitivity of the X-ray detector has improved,effects of after-images resulting from an afterglow of scintillatorshave become notable, thus decreasing the time resolution and the qualityof pictures. Specifically, such X-ray detectors include scintillatorsthat generate fluorescent when receiving X-rays, detecting the X-rays bydetecting the fluorescent with photodetecting means such as aphotodiode. The fluorescent of the scintillators, however, does not stopimmediately even after termination of the X-ray irradiation, toattenuate together with a delay in response, causing afterglow. Suchafterglow is mixed in projection data to be sampled, causingafter-images (artifact). Several methods are presented to correct theafterglow causing the after-images.

One of the methods is a method of correcting the shortest time-constantcomponent at any time (refer to Japanese Examined Patent Publication No.7-090024). Another method is a correction method using lineartransformation of detector output (refer to Japanese Examined PatentPublication No. 7-102211). Another method is a correction method incorrespondence with plural time constants at any time (refer to JapaneseUnexamined Patent Publication No. 6-90945). Another method is acorrection method using convolution integration (refer to JapaneseUnexamined Patent Publication No. 6-343629).

The method disclosed in Japanese Unexamined Patent Publication No.6-90945 is to acquire the time constant of the longest impulse responsetime and its component using a device including a radiation detectorhaving an exponential impulse response determined by plural differenttime constants, and after eliminating the component, to acquire the nextlongest time constant and its component ratio and eliminate thecomponent, wherein the process is repeated until influence of afterglowcomponents is lost. It is described that the data of the time constantsand their components are obtained in a factory by operating a CTapparatus with no object of tomogram present in an imaging opening. Inother words, the impulse response data is collected only before shippingproducts from a factory.

However, since the characteristics of the X-ray detector of detectingafterglow and so on vary depending on environments including temperatureduring photographing of an object and secular change, the aforesaidmethods are possibly unable to sufficiently eliminate afterglowcomponents.

Such X-ray CT apparatus are required to accurately extract and eliminateafterglow components contained in projection data for further reducingeffects of afterglow.

DISCLOSURE OF INVENTION

An object of the present invention is to reduce the influence ofafterglow in an X-ray CT apparatus.

According to the present invention, an X-ray CT apparatus comprising anX-ray source for irradiating X-rays to an object and an X-ray detectorarranged to face the X-ray source and detecting the amount oftransmitted X-rays of the object as projection data. Further comprising,to solve above-described problems, basic-data acquisition means foracquiring response data of the projection data as basic data with noobject present every time before the image of the object is acquired,analyzing means for breaking down an afterglow component of the acquiredbasic data into a plurality of time constants and their componentratios, storage means for storing the broken-down time constants andcomponent ratios, correcting means for extracting an afterglow componentof the projection data on the basis of the stored time constants andcomponent ratios during radiography of the object and eliminating theextracted afterglow component of the projection data from the projectiondata to produce corrected projection data, reconstructing means forreconstructing an image using the produced corrected projection data,and display means for displaying the reconstructed image.

The above-described problems, also, are solved by a method or a programfor correcting afterglow of an X-ray CT apparatus having an X-ray sourcefor applying X-rays to an object and an X-ray detector arranged to facethe X-ray source for detecting the amount of transmitted X-rays of theobject as projection data. The method or the program comprises, abasic-data acquisition step of acquiring response data of the projectiondata with no object as basic data every time before the image of theobject is acquired, an analyzing step for breaking down an afterglowcomponent of the acquired basic data into a plurality of time constantsand their component ratios, a storing step of memorizing the analyzedtime constants and component ratios, a correcting step of extracting anafterglow component of the projection data on the basis of the storedtime constants and component ratios during radiography of the object andremoving the extracted afterglow component of the projection data fromthe projection data to produce corrected projection data, areconstructing step of reconstructing an image using the producedcorrected projection data, and a displaying step of displaying thereconstructed image.

According to the present invention, since an afterglow component isbroken-down into a plurality of time constants and their componentratios on the basis of the basic data every time the image of the objectis acquired, the component ratio for the time constants can beaccurately determined, so that an afterglow signal component isaccurately calculated. Since corrected projection data in which anafterglow component is eliminated from the projection data are acquiredby using the accurate component ratio for the time components, theeffects of afterglow can be further reduced, whereby the occurrence ofartifact is reduced and the time resolution of the X-ray CT apparatus isimproved.

The time constants and their component ratio of the previously acquiredcorrected projection data may be memorized in the storage means and maybe used when new corrected projection data are sequentially acquired.

With such an arrangement, the time constants and their component ratioof the latest corrected projection data are used for new correctedprojection data to be acquired the next time. Therefore, since forexample, the amount of X-rays for the object in the slice positionadjacent to the previous CT image is substantially the same as that ofthe previous one, the afterglow components caused thereby are alsosubstantially the same. In such a case, since there is no need to storeprevious data accumulatively, the memory capacity used in the correctingmeans can be reduced.

An X-ray CT apparatus may comprise, an X-ray source for irradiatingX-rays to an object, an X-ray detector arranged to face the X-ray sourcefor detecting the amount of transmitted X-rays through the object asprojection data, actual-measurement acquisition means for acquiring theprojection data of a step response, as an actual measurement, whencontinuous X-rays are irradiated to the X-ray detector with no objectpresent and thereafter the irradiation is stopped; analyzing means forbreaking down the step response of the acquired actual measurement intoan impulse response, representing the calculation of the step responsethrough the convolution integration of the analyzed impulse response,and calculating a plurality of time constants and their component ratiosasymptotically and recursively that make the error between the actualmeasurement and the calculation lower than a set value, storage meansfor storing the calculated time constants and component ratios,correcting means for eliminating an afterglow component of the storedprojection data from the projection data to produce corrected projectiondata during radiography of the object, reconstructing means forreconstructing an image using the produced corrected projection data,and display means for displaying the reconstructed image.

Accordingly, the component ratios for the time constants are obtained byrepeating the recursive operation until the error becomes a set value orless. Accordingly, the accuracy of the time constants and theircomponent ratios is ensured, allowing high-reliability afterglowcorrection.

An X-ray CT apparatus may comprise, an X-ray source for applying X-raysto an object, an X-ray detector arranged to face the X-ray source fordetecting the amount of transmitted X-rays through the object asprojection data, basic-data acquisition means for acquiring responsedata of the projection data as basic data in advance with no objectpresent, analyzing means for analyzing an afterglow component of theacquired basic data into a plurality of time constants and theircomponent ratios by using a genetic algorithm, storage means for storingthe analyzed time constants and component ratios, correcting means forextracting an afterglow component of the projection data on the basis ofthe stored time constants and component ratios during radiography of theobject and eliminating the extracted afterglow component of theprojection data from the projection data to produce corrected projectiondata, reconstructing means for reconstructing an image using theproduced corrected projection data, and display means for displaying thereconstructed image.

Accordingly, the use of the genetic algorithm when determining thecomponent ratios for the time constants by a recursive operationaccelerates the convergence of the recursive operation, thus providingaccurate component ratios at an early stage.

The acquisition of the basic data in the response characteristic, thecalculation of the component ratios for the time constants, and thecorrection of the projection data may be performed for each channel forthe X-ray detectors having multiple channels, for example, approximatelyone thousand channels.

For an X-ray detector providing multiple modules having a detectingsection corresponding to multiple channels made of the same element, theacquisition of the basic data and the calculation of the componentratios for the time constants may be performed only for part of thechannels representing each module, while common correction may be madefor the projection data corresponding to the modules. Specifically,since the channels made of the same element have a similar responsecharacteristic, the time required for calculation of the componentratios for the time constants is reduced by correcting each channel onthe basis of the basic data of a representative channel, and thecapacity of a memory for storing them can also be reduced. For example,in an X-ray detector having an X-ray detecting section for 16 channelsas one module, the basic data may be acquired only for one or morepartial channels of each module.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an explanatory diagram of an X-ray CT apparatus including acorrecting means for removing afterglow, according to the embodiment ofthe present invention.

FIG. 2 is a flowchart for explaining the operation of the X-ray CTapparatus shown in FIG. 1.

FIG. 3 is an explanatory diagram of a method for determining impulseresponse by the measurement of step response, shown in the flowchart ofFIG. 2.

FIG. 4 is an explanatory diagram of a method for determining an impulseresponse from a component ratio of time constants, shown in theflowchart of FIG. 2.

FIG. 5 is an explanatory diagram of a correcting method shown in FIG. 2and a method for determining the component ratio of the time constants,necessary to determine the impulse response shown in FIGS. 3 and 4.

FIG. 6 is an explanatory diagram of an algorithm for eliminatingafterglow.

FIG. 7 is an explanatory diagram of a method for finding a componentratio for time constants using genetic algorithm to determine acalculation value of an impulse response for the same purpose as that ofFIG. 5.

FIG. 8 is an explanatory diagram of a gene arrangement in the geneticalgorithm described in FIG. 7.

FIG. 9 is an explanatory diagram for showing change of an evaluationfunction in FIG. 7.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring to the drawings, embodiments of an X-ray CT apparatusincorporating the present invention will be specifically described.

According to the embodiments of the invention, an X-ray tube is used asan X-ray source. In this specification, afterglow is the output(projection data) of an X-ray detector, while an after-image is given asan image after the afterglow has been reconstructed.

(First Embodiment)

Referring to FIG. 1, the basic structure of the X-ray CT apparatus is asfollows. X-rays 2 are applied from an X-ray tube 105 to captureprojection data representing the amount of attenuation of the X-rays 2that have passed through an object 1 and taken in an X-ray detector 106arranged to face the X-ray tube 105 interposing the object 1therebetween and having multiple channels 107.

An image is reconstructed with a reconstructing means 103 basis on theprojection data and displayed with a tomogram display means 104.

Basic data about the response characteristic of the projection data areacquired for every channel 107 under a state that object 1 does notexist. The apparatus comprises an analyzing means 100 for breaking downthe basic data for every channel 107 and decomposing the responsecharacteristic into components for every time-constant, a storage means101 for memorizing the component ratio of time constants, and acorrecting means 102 for converting the projection data to correctedprojection data in which the effects of the after-image are removedduring radiography of the object 1.

Referring next to FIG. 2, a method for correcting the after-image in theX-ray CT apparatus of FIG. 1 will be described.

The determination of a step response (Step 50) and the calculation of animpulse response (Step 51), shown in FIG. 2, are carried out by theanalyzing means 100. The correction of the projection data (raw data)(Step 54) is carried out by the correcting means 102. The storage of theimpulse response (Step 52) is carried out by the storage means 101.

The step response is measured with no object 1 present and thus obtainedprojection data are used as basic data (Step 50).

The correcting means has a stop means for shutting off the output ofX-rays at a predetermined arbitrary sampling number or time. The stopmeans stops the output from the X-ray tube 105, shown in FIG. 1, at anytime, e.g., at the point in time when the half of scanning time haspassed after the X-ray CT apparatus has emitted the X-rays. From thedata of determination of the step response thus obtained (Step 50), thecomponent ratios for the time constants regarding the impulse response68, shown in FIG. 3, is analyzed to calculate the impulse response (Step51). The component ratio of the time constants of the impulse response68 is stored for every channel (Step 52).

When the object is actually subjected to radiography (Step 53), as shownin FIG. 2, projection data are taken from the X-ray detector 106 of FIG.1 during scanning. The projection data are corrected every time they aretaken in (Step 54).

The corrected projection data are reconstructed as in general X-ray CTapparatus (Step 55) to construct the tomogram of the object 1. Thetomogram is displayed on a tomogram display means 104 (Step 56).

A method for calculating the impulse response from the determination ofthe step response shown in FIG. 2 will be described.

As referred to FIG. 3, a step response 66 serving as the base of thecorrection is radiographed and acquired as basic data with no object 1present.

The application of X-rays for obtaining the step response 66 and theresponse of the X-ray detector 106, shown in FIG. 1, are as follows.

A step input 65 is the same as continuous impulse inputs 67, as shown inFIG. 3(a). Since the impulse response 68 is the result of output on theassumption that ideal impulses were inputted, as shown in FIG. 3(c).Since the step response 66 is an output from continuous inputs, the stepresponse 66 can be expressed as a convolution integral of the impulseresponse 68. Conversely, if the impulse response 68 can be calculated,the step response 66 is determined.

Since the ON/OFF control of the X-ray tube 105, shown in FIG. 1, isdifficult, it is difficult to obtain the impulse response 68 shown inFIG. 3(c) as compared with the step response 66 shown in FIG. 3(b).

Specifically, since the pulse width of the step input 65 is longer thanthat of the impulse input 67, the control becomes easy and the stepresponse 66 can be determined more easily.

The impulse response 68 has an exponential characteristic having acomponent ratio of multiple time constants, as expressed in thefollowing equationX(t)=ΣSi·exp(−t/τi)  (1),whereX(t) is the impulse response, t designates the time from impulse input,Si(i=1, 2, . . . n) does the component ratio of time constants, and τidoes different time constants as many as n. Symbol i denotes a naturalnumber assigned to the respective time constants. Thus, when a set ofthe component ratio Si of time constants and the n different timeconstants is determined, the impulse response 68 can be reproduced.Further, the step response 66 can be reproduced by convolutionintegration thereof.

As one of methods of determining the set of the component ratio Si ofthe time constants and the n different time constants τi, the ndifferent time constants τi are predetermined in geometric progressionor logarithmically in advance. The distribution of the component ratioSi corresponding to the time constants is estimated and assumedtemporarily on the basis of an empirical value or the like.

A method for finding the calculation of the impulse response 68 from thestep response 66 shown in FIG. 3 will now be described.

The relationship between the step response 66 in FIG. 3(b) and theimpulse response 68 in FIG. 3(c) is expressed as convolution integral,as in the equation $\begin{matrix}{{{Z(t)} = {\sum\limits_{i = 0}^{t}{\times \left( {t - i} \right)\left( {t > t_{0}} \right)}}},} & (2)\end{matrix}$where

-   -   Z(t): actual measurement of the step response when the time t        has exceeded t₀; and    -   X(t−i): the impulse response at time t and with time-constant        component ratio i.

When the time constant is allotted to abscissa and the component ratiois allotted to ordinate, the distribution 70 of the component ratios Siof the time constants is as shown in FIG. 4, wherein the integral is 1.The distribution 70 of the component ratio Si of the time constants hasdose correlations respectively with the impulse response 68 and the stepresponse 66 shown in FIG. 3. Therefore, when the distribution 70 of thecomponent ratio Si of the time constants related to the impulse responseis determined, the impulse response 68 and the step response 66, shownin FIG. 3, can be determined. As shown in FIG. 4, a plurality ofcomponent ratios Si are, for example, of the time constants of from 0.1ms to 1,000 ms.

Referring to the flowchart of FIG. 5, a method for finding thedistribution 70 of the component ratios Si of the time constants and thecalculated value X(t) of the impulse response from the actualmeasurement Z(t) of actually measured step response will be described.

The plurality of time constants and the initial values of the respectivecomponent ratios of the time constants related to the impulse responseare arbitrarily set (Step 71). A temporary value of the impulse responseX(t) is found by calculation of Equation (1) (Step 72). The calculationZ′(t) of the step response is found (Step 74) by convolution integrationof Equation (2) (Step 73). The square error between the calculationZ′(t) of the step response and the actual measurement Z(t) of the stepresponse (Step 75) is set as evaluation function φ(Si), as in thefollowing equationφ(Si)=(Z(t)−Z′(t))²  (3)

The impulse response is recalculated using the equation (1) depending onthe magnitude of evaluation function φ(Si) while the set of thecomponent ratios Si of the time constants is changed in accordance with,for example, random numbers little by little by using a feedback loopfor correcting the distribution 70 of the component ratios Si of thetime constants shown in FIG. 4. Then the error between the calculationZ′(t) of the step response and the actual measurement Z(t) of the stepresponse is evaluated using the equation (3) (Step 76).

Although the evaluation function φ(Si) is asymptotically decreased asdescribed above, in general, the evaluation function φ(Si) cannot alwaysbe reduced to zero. Thus, the distribution 70 of the component ratios Siof the time constants shown in FIG. 4, which reproduces the stepresponse 66 of FIG. 3, is determined by setting a threshold of theevaluation function φ(Si) becomes sufficiently practically low andenabling escape from the feedback loop when the evaluation functionφ(Si) becomes the threshold or less(Step 70). The calculation X(t) ofthe impulse response is determined by the equation (1) on the basis ofthe distribution 70 of the component ratios Si of the time constants(Step 77).

The method of acquiring corrected projection data by correcting theprojection data (measurement data) will then be described.

Referring to FIG. 6, the measurement data concerning afterglow and theamount of luminescence can be expressed by allotting time to abscissaand the intensity of luminescence to ordinate.

Corrected projection data DA(k) for the k-th sampling number can begiven by the equation $\begin{matrix}{{{DA}(k)} = {{{DB}(k)} - {\sum\limits_{i = 0}^{n}{{Si} \cdot {{Bi}(k)}}}}} & (4)\end{matrix}$where

-   -   DA(k): corrected projection data of the k-th sampling number,        where DA(0)=DB(0);    -   DB(k): measurement data of the k-th sampling number;    -   Si: the ratio of components for the i-th time constant; and    -   Bi(k): contribution of afterglow of the k-th sampling number and        the i-th time constant, wherein Bi(0)=0.

Specifically, as expressed by the equation (4), Bi(k) is thecontributory part of the afterglow for every component ratio of the i-thtime constant. When the sum of all contributory parts Bi(k) of theafterglow for every component ratio of the i-th time constants issubtracted from the present projection data DB(k), the correctedprojection data DA(k) is obtainable.

The calculation of the corrected projection data can be achieved with arecursive filter.

The corrected projection data DA(k) is calculated for every channel 107of the X-ray detector 106 shown in FIG. 1.

The contributory parts Bi(k) of the afterglow for every component ratioof the time constants at the time can be calculated by the followingequation with respect to the range shown in FIG. 6.Bi(k)=(Bi(k−1)+DA(k−1)·exp(−Δt/τi)  (5),where

-   -   Bi(k−1): contribution of the afterglow for every component ratio        of the time constants of the (k−1)th sampling number immediately        before the k-th sampling number;    -   DA(k−1): corrected projection data of the (k−1)th sampling        number immediately before the k-th sampling number;    -   Δt: time interval between the k-th sampling number and the        (k−1)th sampling number immediately therebefore; and

τi: i-th time constant (τ0=0.1 ms, . . . τ4=1,000 ms).

Specifically, as expressed by the equation (5), the contributory partsBi(k) of the afterglow for every component ratio of time constants atthe k-th sampling number is found by multiplying the sum of thecontributory part Bi(k−1) of the afterglow for time constant τi at the(k−1)th sampling number immediately before the k-th sampling number andcorrected projection data DA(k−1) at the (k−1)the sampling numberimmediately before the k-th sampling number by the attenuationexp(−Δt/τi) of Δt corresponding to the time constant Δi.

The calculations by the equations (4) and (5) are performed for everychannel 107 of the X-ray detector 106 shown in FIG. 1, to convent intothe corrected projection data DA(k).

The corrected projection data DA(k) is stored in the storage means 101shown in FIG. 1 for every channel 107 and every component ratio of thetime constants to update the result at every calculation.

An image after correction is formed using the corrected projection dataDA(k) with the reconstructing means 103, shown in FIG. 1.

According to the embodiment, as described above, because the timeconstants that indicate afterglow components are determined on the basisof the basic data acquired with no object present; thus, the componentratios for the time constants can be accurately obtained, allowingaccurate calculation of the afterglow component. Since correctedprojection data is acquired by using the accurate component ratios forthe time constants, the effects of afterglow can be decreased, thusreducing the occurrence of artifacts to improve the time resolution ofdevices.

With the correcting means, new corrected projection data is acquired,for every sampling time, by subtracting the sum of the values found bymultiplying the value obtained by breaking down the previously acquiredcorrected projection data depending on the component ratios for the timeconstants and the value of the afterglow component for every timeconstants by the time of sampling multiple times before at thecalculation of the corrected projection data by the respectiveattenuations of the time constants from the projection data at thesampling time for the correction object. Accordingly, if the respectiveafterglow components of the time constants at the sampling time when thecorrected projection data is previously calculated and the correctedprojection data at that time are found, corrected projection data at thelatest sampling time can be acquired. Therefore, there is no need toaccumulate the preceding data for storage, decreasing necessary memorycapacity.

Since a recursive operation is done until the error between thecalculation of a step response represented by convolution integration ofthe impulse response obtained by using the component ratios for the timeconstants that are calculated on the basis of the basic data and theactual measurement of the step response obtained as the basic databecomes a predetermined threshold or less, the accuracy of the componentratios for the time constants is ensured, thus allow high-reliabilityafterglow correction.

(Second Embodiment)

A second embodiment of the X-ray CT apparatus incorporating theinvention will be described. The description of the same parts as thoseof the first embodiment will be omitted and only differences will bedescribed. The embodiment is characterized in that a genetic algorithmis applied to calculate the component ratio of the time constants forthe impulse response on the basis of the basic data about the stepresponse obtained with no object present. The flowchart of FIG. 7 showsan example of the application of a genetic algorithm as analyzing meansfor the impulse response 68 and the step response 66 for finding thecalculation of the impulse response 68 in FIG. 3. The genetic algorithmis one of general methods for optimization.

A gene arrangement Sim, shown in FIG. 7, uses the component ratio Si forthe time constants as the gene arrangement as shown in FIG. 8. Thesquare error φ(Si) between the calculation Z′(t) of the step responsecalculated by the impulse response X(t) and the actual measurement Z(t)of the step response obtained as basic data (equation (2)) is set as theevaluation function (Equation (3)).

Further, the gene arrangement, the component ratio of the time constant,having the evaluation function φ(Si) improved in the generationalternating loop of the gene algorithm shown in FIG. 7, or is calculatedasymptotically. In the genetic algorithm, a plurality of genearrangements (Si1, Si2, Si3, . . . Sim) are used.

As shown in FIG. 7, the gene arrangements Si1 to Sim (m=10) are set atrandom as the initial state (Step 82). Of the generation alternatingloop, for the expressive form, the calculation Z′(t) of the stepresponse is calculated for every gene arrangement by the equation (2),described in FIG. 3 (Step 83).

The calculations are sorted by error evaluation in ascending order ofthe sum of the squares of the error between the actual measurement Z(t)of the step response and the calculation Z′(t) of the step response,wherein when the evaluation function φ(Si) is larger than the threshold(=2), the process shifts to step 85 (Step 84). In this error evaluation,of the evaluation functions φ(Si1), φ(Si2), . . . φ(Si10) for theimpulse response X(t), a gene arrangement with the higher evaluationfunction is increased in the probability of surviving to the nextgeneration, thus more preferable gene arrangements are selected.

The low-order half gene arrangements of the gene arrangements Si1 toSi10 are killed depending on the degree of the error and the upper-orderhalf gene arrangements are increased to double by a selecting operation.Thus, poor gene arrangements are deleted and preferable genearrangements are left (Step 85).

Part of the arrangements is exchanged with other gene arrangements indescending order of preference of the evaluation function by acrossing-over operation (Step 86). Mutation is generated in part of thegene arrangements by a mutating operation (Step 87). The generationalternating loop is repeated to asymptotically decrease the evaluationfunction φ(Si).

As a result of the error evaluation in the generation alternating loop,when the evaluation function φ(Si) becomes smaller than the threshold(=2), the process gets out of the generation alternating loop (Step 84),thus providing a gene arrangement 81 with a minimum error.

In the embodiment of the invention shown in FIG. 7, the calculation ofthe evaluation functions φ(Si) of the gene arrangements Si1 to Si10 forthe time constant 0.1 ms for every generation alternating loop leads theresult in FIG. 9. As shown in FIG. 9, in the case of the embodiment ofFIG. 7, the evaluation functions φ(Si) of all the gene arrangements Si1to Si10 become smaller than the set threshold (=2) in the 150thgeneration of the generation alternating loop, thus, a gene arrangementwith a minimum error is obtained.

Of course, in general, the evaluation function φ(Si) cannot necessarilybe made zero; however, by setting the threshold so that the evaluationfunction φ(Si) becomes sufficiently small in practice and by getting theprocess out of the generation alternating loop, the distribution 70 ofthe component ratios Si for time constants that represents the stepresponse 66 in FIG. 3 can be determined.

According to the embodiment of FIGS. 7 to 9, by using the componentratios for the time constants as gene arrangements and calculating genearrangements with a decreased error, i.e., the component ratios for thetime constants asymptotically and recursively to calculate the impulseresponse 68 automatically with the generation alternating loop by agenetic algorithm, a high-quality X-ray CT apparatus can be achievedwhich has no image noise caused by an after-image due to afterglow orthe like and no reduction in time resolution.

As described above, according to the embodiment, the same advantages asthose of the above-described first embodiment are demonstrated. Inaddition thereto, there are effects of accelerating the convergence ofthe recursive operation and thus providing accurate component ratios atan early stage because it uses a genetic algorithm in obtainingcomponent ratios for time constants by a recursive operation.

The X-ray tube used in the X-ray CT apparatus according to the inventionis merely an embodiment of an X-ray source and is not limited thereto,and it is clear that, electronic-beam sources, radiation sources(radioisotope) and so on may be used to obtain similar effects.

The acquisition of the basic data and the calculation of the componentratios of time constants, described above, may be performed during theoperation of the X-ray CT apparatus to cope with environments such astemperature in which the X-ray detector is used and the ageddeterioration of the X-ray detector. For example, they may be performedduring so-called air calibration done immediately before everyacquisition of the image of an object. Further, they may be performed ata stage of factory shipment of the X-ray CT apparatus in order to copewith the variations in the characteristics of the X-ray detectors.

According to the embodiments, the component ratio of the time constantsis calculated with respect to all the channels of the X-ray CTapparatus. However, when the X-ray detector has a plurality of modulesincluding an X-ray detecting section in correspondence with theplurality of channels, the calculation of the component ratio may beperformed only for a part of the channels of each module and thecorrection of the channels in a common module may be performed using acommon component ratio. In other words, because X-ray detectors in anidentical module formed of the same elements have a similar responsecharacteristic, the time required for calculating the component ratio ofthe time constants is reduced, the capacity of a memory for memorizingthe component ratios can also be reduced. Also in this case, althoughthe calculation of corrected projection data during object radiographyis performed at every individual channel, the recursive filteroperations for the individual channel are the same.

1. An X-ray CT apparatus comprising: an X-ray source for applying X-raysto an object; an X-ray detector arranged to face the X-ray source fordetecting the amount of transmitted X-rays of the object as projectiondata; basic-data acquisition means for acquiring response data of theprojection data as basic data with no object in advance every time theimage of the object is acquired; analyzing means for analyzing anafterglow component of the acquired basic data into a plurality of timeconstants and their component ratios; storage means for storing theanalyzed time constants and component ratios; correcting means forextracting an afterglow component of the projection data on the basis ofthe stored time constants and component ratios during radiography of theobject and removing the extracted afterglow component of the projectiondata from the projection data to produce corrected projection data;reconstructing means for reconstructing an image using the producedcorrected projection data; and display means for displaying thereconstructed image.
 2. An X-ray CT apparatus according to claim 1,wherein the storage means stores the time constants and their componentratios of the previously acquired corrected projection data and usesthem when acquiring new corrected projection data sequentially.
 3. AnX-ray CT apparatus comprising: an X-ray source for applying X-rays to anobject; an X-ray detector arranged to face the X-ray source fordetermining the amount of transmitted X-rays of the object as projectiondata; actual-measurement acquisition means for acquiring the projectiondata of a step response as an actual measurement when continuous X-raysare irradiated to the X-ray detector with no object present andthereafter the irradiation is stopped; analyzing means for analyzing thestep response of the acquired actual measurement into an impulseresponse, representing the calculation of the step response through theconvolution integration of the analyzed impulse response, andcalculating a plurality of time constants and their component ratiosasymptotically and recursively that make the error between the actualmeasurement and the calculation lower than a set value; storage meansfor storing the calculated time constants and component ratios;correcting means for removing an afterglow component of the storedprojection data from the projection data to produce corrected projectiondata during radiography of the object; reconstructing means forreconstructing an image using the produced corrected projection data;and display means for displaying the reconstructed image.
 4. An X-ray CTapparatus comprising: an X-ray source for applying X-rays to an object;an X-ray detector arranged to face the X-ray source for determining theamount of transmitted X-rays of the object as projection data;basic-data acquisition means for acquiring response data of theprojection data as basic data with no object in advance; analyzing meansfor analyzing an afterglow component of the acquired basic data into aplurality of time constants and their component ratios by using agenetic algorithm; storage means for storing the analyzed time constantsand component ratios; correcting means for extracting an afterglowcomponent of the projection data on the basis of the stored timeconstants and component ratios during radiography of the object andremoving the extracted afterglow component of the projection data fromthe projection data to produce corrected projection data; reconstructingmeans for reconstructing an image using the produced correctedprojection data; and display means for displaying the reconstructedimage.
 5. An X-ray CT apparatus according to claim 4, wherein theanalyzing means calculates gene arrangements having an evaluationfunction improved through a generation alternating loop by the geneticalgorithm asymptotically and recursively, with the component ratios forthe time constants as the gene arrangements and with the error between astep response represented on the basis of an impulse response as aresult of a calculation and the step response acquired as the basic dataas the evaluation function, to determine the time constants and theircomponent ratios.
 6. An X-ray CT apparatus according to claim 1, whereinthe X-ray detector comprises a plurality of modules having an X-raydetecting section corresponding to a plurality of channels, and thecomponent ratios for the time constants are determined for part of thechannels representing the modules.
 7. An X-ray CT apparatus according toclaim 1, wherein the time components and their component ratios aredetermined for each of the plurality of the cannels of the X-raydetector.
 8. A method for correcting afterglow of an X-ray CT apparatushaving an X-ray source for applying X-rays to an object and an X-raydetector arranged to face the X-ray source for determining the amount oftransmitted X-rays of the object as projection data, comprising: abasic-data acquisition step of acquiring response data of the projectiondata as basic data with no object present in advance every time theimage of the object is acquired; an analyzing step of analyzing anafterglow component of the acquired basic data into a plurality of timeconstants and their component ratios; a storing step of storing theanalyzed time constants and component ratios; a correcting step ofextracting an afterglow component of the projection data on the basis ofthe stored time constants and component ratios during radiography of theobject and removing the extracted afterglow component of the projectiondata from the projection data to produce corrected projection data; areconstructing step of reconstructing an image using the producedcorrected projection data; and a displaying step of displaying thereconstructed image.
 9. A method for correcting afterglow of an X-ray CTapparatus according to claim 8, wherein the storing step comprises theprocess of storing the time constants and their component ratios of thepreviously acquired corrected projection data and using them whenacquiring new corrected projection data sequentially.
 10. A method forcorrecting afterglow of an X-ray CT apparatus having an X-ray source forapplying X-rays to an object and an X-ray detector arranged to face theX-ray source for determining the amount of transmitted X-rays of theobject as projection data, comprising: an actual-measurement acquisitionstep of acquiring the projection data of a step response, as an actualmeasurement, when continuous X-rays are irradiated to the X-ray detectorwith no object present and thereafter the irradiation is stopped; ananalyzing step of analyzing the step response of the acquired actualmeasurement into an impulse response, representing the calculation ofthe step response through the convolution integration of the analyzedimpulse response, and calculating a plurality of time constants andtheir component ratios asymptotically and recursively that make theerror between the actual measurement and the calculation lower than aset value: a storing step of storing the calculated time constants andcomponent ratios; a correcting step of removing an afterglow componentof the stored projection data from the projection data to producecorrected projection data during radiography of the object; areconstructing step of reconstructing an image using the producedcorrected projection data; and a displaying step of displaying thereconstructed image.
 11. A method for correcting afterglow of an X-rayCT apparatus having an X-ray source for applying X-rays to an object andan X-ray detector arranged to face the X-ray source for determining theamount of transmitted X-rays of the object as projection data,comprising: a basic-data acquisition step of acquiring response data ofthe projection data as basic data with no object present in advance; ananalyzing step of analyzing an afterglow component of the acquired basicdata into a plurality of time constants and their component ratios byusing a genetic algorithm; a storing step of storing the analyzed timeconstants and component ratios; a correcting step of extracting anafterglow component of the projection data on the basis of the storedtime constants and component ratios during radiography of the object andremoving the extracted afterglow component of the projection data fromthe projection data to produce corrected projection data; areconstructing step of reconstructing an image using the producedcorrected projection data; and a displaying step of displaying thereconstructed image.
 12. A method for correcting afterglow of an X-rayCT apparatus according to claim 11, wherein the analyzing stepcomprising the process of calculating gene arrangements having anevaluation function improved through a generation alternating loop bythe genetic algorithm asymptotically and recursively, with the componentratios for the time constants as the gene arrangements and with theerror between a step response represented on the basis of an impulseresponse as a result of a calculation and the step response acquired asthe basic data as the evaluation function, to determine the timeconstants and their component ratios.
 13. A program for correctingafterglow of an X-ray CT apparatus having an X-ray source for applyingX-rays to an object and an X-ray detector arranged to face the X-raysource for determining the amount of transmitted X-rays of the object asprojection data, comprising: a basic-data acquisition step of acquiringresponse data of the projection data as basic data with no objectpresent in advance every time the image of the object is acquired; ananalyzing step of analyzing an afterglow component of the acquired basicdata into a plurality of time constants and their component ratios; astoring step of storing the analyzed time constants and componentratios; a correcting step of extracting an afterglow component of theprojection data on the basis of the stored time constants and componentratios during radiography of the object and removing the extractedafterglow component of the projection data from the projection data toproduce corrected projection data; a reconstructing step ofreconstructing an image using the produced corrected projection data;and a displaying step of displaying the reconstructed image.
 14. Aprogram for correcting afterglow of an X-ray CT apparatus according toclaim 13, wherein the storing step comprises the process of storing thetime constants and their component ratios of the previously acquiredcorrected projection data and using them when acquiring new correctedprojection data sequentially.
 15. A program for correcting afterglow ofan X-ray CT apparatus having an X-ray source for applying X-rays to anobject and an X-ray detector arranged to face the X-ray source fordetermining the amount of transmitted X-rays of the object as projectiondata, comprising: an actual-measurement acquisition step of acquiringthe projection data of a step response, as an actual measurement, whencontinuous X-rays are applied to the X-ray detector with no objectpresent and thereafter the application is stopped; an analyzing step ofanalyzing the step response of the acquired actual measurement into animpulse response, representing the calculation of the step responsethrough the convolution integration of the analyzed impulse response,and calculating a plurality of time constants and their component ratiosasymptotically and recursively that make the error between the actualmeasurement and the calculation lower than a set value; a storing stepof storing the calculated time constants and component ratios; acorrecting step of removing an afterglow component of the storedprojection data from the projection data to produce corrected projectiondata during radiography of the object; a reconstructing step ofreconstructing an image using the produced corrected projection data;and a displaying step of displaying the reconstructed image.
 16. Aprogram for correcting afterglow of an X-ray CT apparatus having anX-ray source for applying X-rays to an object and an X-ray detectorarranged to face the X-ray source for determining the amount oftransmitted X-rays of the object as projection data, comprising: abasic-data acquisition step of acquiring response data of the projectiondata as basic data with no object present in advance; an analyzing stepof analyzing an afterglow component of the acquired basic data into aplurality of time constants and their component ratios by using agenetic algorithm; a storing step of storing the analyzed time constantsand component ratios; a correcting step of extracting an afterglowcomponent of the projection data on the basis of the stored timeconstants and component ratios during radiography of the object andremoving the extracted afterglow component of the projection data fromthe projection data to produce corrected projection data; areconstructing step of reconstructing an image using the producedcorrected projection data; and a displaying step of displaying thereconstructed image.
 17. A program for correcting afterglow of an X-rayCT apparatus according to claim 16, wherein the analyzing stepcomprising the process of calculating gene arrangements having anevaluation function improved through a generation alternating loop bythe genetic algorithm asymptotically and recursively, with the componentratios for the time constants as the gene arrangements and with theerror between a step response represented on the basis of an impulseresponse as a result of a calculation and the step response acquired asthe basic data as the evaluation function, to determine the timeconstants and their component ratios.